On the interaction of a planar shock with an polygon

Abstract

The interaction of a planar shock wave ($M\approx 1.2$) with an $\text{SF}_{6}$ polygonal inhomogeneity surrounded by air is experimentally investigated. Six polygons including a square, two types of rectangle, two types of triangle, and a diamond are generated by the soap film technique developed in our previous work, in which thin pins are used as angular vertexes to avoid the pressure singularities caused by the surface tension. The evolutions of the shock-accelerated $\text{SF}_{6}$ polygons are captured by a high-speed schlieren system from which wave systems and the interface characteristics can be clearly identified. Both regular and irregular refraction phenomena are observed outside the volume, and more complex wave patterns, including transmitted shock, refracted shock, Mach stem and the interactions between them, are found inside the volume. Two typical irregular refraction phenomena (free precursor refraction, FPR, and free precursor von Neumann refraction, FNR) are observed and analysed, and the transition from FPR to FNR is found, providing the experimental evidence for the transition between different wave patterns numerically found in the literature. Combined with our previous work (Zhai et al., J. Fluid Mech., vol. 757, 2014, pp. 800–816), the reciprocal transitions between FPR and FNR are experimentally confirmed. The velocities and trajectories of the triple points are further measured and it is found that the motions of the triple points are self-similar or pseudo-stationary. Besides the shock dynamics phenomena, the evolutions of these shocked heavy polygonal volumes, which are quite different from the light ones, are captured and found to be closely related to their initial shapes. Specifically, for square and rectangular geometries, the different width–height ratios result in different behaviours of shock–shock interaction inside the volume, and subsequently different features for the outward jet and the interface. Quantitatively, the time-variations of the interface scales, such as the width and the normalized displacements of the edges, are obtained and compared with those from previous work. The comparison illustrates the superiority of the interface formation method and the significant effect of the initial interface shape on the interface features. Furthermore, the characteristics of the vortex core, including the velocity and vortex spacing, are experimentally measured, and the vortex velocity is compared with those from some circulation models to check the validity of the models. The results in the present work enrich understanding of the shock refraction phenomenon and the database of research into Richtmyer–Meshkov instability (RMI).